is entirely with Peyton Farquhar. It is quite possible to feel sympathy with an enemy after he has been defeated. He is, after all, a fellow human being. Perhaps it was Bierce's intention to emphasize that Farquhar is a fellow human being and that it is tragic that men have to be so cruel to one another. This feeling was particularly common during the Civil War, when men who had nothing against each other found themselves enemies without quite understanding why or how it had happened.

We do not feel sympathy for Peyton Farquhar because of the cause he represents but in spite of it. We feel sympathy for the man because we can easily understand his feelings. He wants to live and to return to his wife and his home. We cannot even condemn his intention to burn down the Owl Creek bridge because it shows his remarkable courage to attack the Union army single-handedly. It is natural to feel sympathy for the underdog, and Farquhar is certainly the underdog in this story. The narrator describes the large assemblage of Union soldiers who are all involved in the execution of a single man. They include the following formidable group: 

Midway up the slope between the bridge and fort were the spectators--a single company of infantry in line, at "parade rest," the butts of their rifles on the ground, the barrels inclining slightly backward against the right shoulder, the hands crossed upon the stock. 

Ambrose Bierce had an interesting history.  He grew up in Ohio, and he worked for an abolitionist newspaper.  Later, while living in Indiana, he enlisted, and his unit was sent to Virginia to “wrest the pro-Union western Virginia counties away from the rest of Confederate Virginia" (HistoryNet).  For the remainder of the war, Bierce would see and experience some of the terrible realities that would shake his idealism, and in the end, leave him wounded and bitter.

It is safe to say, then, that if Bierce was biased against anything, he is biased against war.  In “Occurrence at Owl Creek Bridge,”  the first scene depicts Farquhar, on the bridge, about to hang.  We don’t know what side he is on, at first, but we are given a few hints that suggest he is probably a Confederate sympathizer.  Later in the story, we learn that he is a plantation owner who has been trying to blow up the bridge.  His information about the bridge came from a Union spy, dressed as a Confederate soldier.

While Bierce does seem to be putting down the Confederates in this part of the story, he also puts the Union down by showing their ridiculous tactics  for “catching” him.  For example, everyone shoots at him and no one hits him.  Also, they stand on the riverbank when they could go into the water and catch him.  If either side comes out worse, it is the Confederate side because they are fooled by the man dressed up in the Confederate soldier’s uniform.